Image reconstruction processes for helical CT scanning are classified into 2D and 3D processes. 2D processes [see Defrise, M., Noo, F., and Kudo, H., “Rebinning-based algorithms for helical cone-beam CT”, Phys. Med. Biol. 46, 2001] estimate parallel tomographic datasets for tilted slices, perform 2D backprojection in each of the tilted slices and reconstruct the volume slice by slice. For 2D processes, geometrical (cone-beam) artifacts increase with the cone-angle (angular extent of the detector in the direction orthogonal to the plane of the gantry rotation). 3D processes reconstruct voxels in the volume directly from projection data without conversion of the backprojection task to intermediate 2D problems. For a given cone angle, images reconstructed with 3D processes generate reduced cone-beam artifacts when compared with images reconstructed with 2D processes.
Traditionally, medical and security CT scanners utilize 2D backprojection reconstruction processes for helical CT due to their ease of implementation, computational efficiency and robustness. New CT scanners increasingly require fast scan speeds and detectors with larger cone-angles, which leads to unsatisfactory level of image artifacts if 2D processes are used to reconstruct images. In order to increase the scanning speed and maintain or improve image quality, it is necessary to transition from using 2D to 3D processes to reconstruct images.
A number of exact and approximate 3D image reconstruction processes have been proposed in the literature. The most widely used 3D approximate process is the Feldkamp Davis Kress (FDK) process, originally proposed in Feldkamp, L. A., Davis, L. C., and Kress, J. W., “Practical cone-beam algorithm”, J. Opt. Soc. Am., Vol. 1 No. 6, 1984, for the case of an axial scan. This process is popular due to its relative ease of implementation, stability and tractable properties. The extension of the FDK process to helical scanning was first proposed in Wang, G., Lin, T., Cheng, P., and Schiozaki, D. M., “A general cone-beam reconstruction algorithm”, IEEE Trans. Med. Imaging, 12, 1993.
The original helical FDK process results in a relatively high level of cone-beam artifacts. Two key enhancements proposed in the literature greatly improve Image Quality and transform the helical FDK into a “quasi-exact” process. First, the tilted plane reconstruction approach described in Yan, M., and Zhang, C., “Tilted plane Feldkamp type reconstruction algorithm for spiral cone beam CT”, Med. Phys. 32 (11), 2005 reduces image artifacts by reducing the mathematical inconsistency between rays used to reconstruct a given voxel. Second, filtering data along lines aligned with the source trajectory (tangential filtering) [Sourbelle, K., and Kalender, W. A., Generalization of Feldkamp reconstruction for Clinical Spiral Cone-Beam CT] significantly reduces cone-beam artifacts. The tangential filtering is derived as an approximation to exact reconstruction processes (such as proposed in Katsevich, A., “An improved exact filtered backprojection algorithm for spiral computed tomography”, Advances in Applied Mathematics, 32, 2004) and modifies the FDK process to be “quasi-exact”.
The quasi-exact version of the helical FDK process as described above is an attractive choice for the modern CT scanner. However, there exist at least three limitations that inhibit implementation of such a process on CT scanners.                1) The FDK processes in the literature are designed for flat or cylindrical detector arrays, which may not be applicable to modern CT scanning systems with unconventional beamline geometry (non-flat, non-cylindrical detector arrays of various geometric (sometimes arbitrary) shapes and with non-uniformly spaced detectors). The quasi-exact FDK process as described in [Kudo, H., Noo, F., and Defrise, M., “Cone-beam filtered-backprojection for truncated helical data”, Phys. Med. Biol. 43, 1998] is only applicable to a flat detector geometry. Therefore, the use of non-conventional detector geometry requires special treatment.        2) The FDK processes in the literature generate aliasing artifacts in scanning systems with large fields of view (FOV) due to the increase in the sampling interval of voxel locations as projected on the detector array with increasing distance from the center of the FOV.        3) The computational complexity of 3D processes is significantly higher than that of 2D processes. Therefore, an efficient process and numerical implementation in combination with a suitable hardware platform are required. In particular, processes and their numerical implementations must be aligned with reconstruction time requirements given the hardware platform.        